Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in PYTHON3):

Solution:
# coding: utf8

def output():    
    print(m)
    for i in range(n):
        print(coord_X[i],coord_Y[i])    

n=int(input()) 
m=0 
while True:  
    m+=1  
    if m*m<n: 
        continue
    if (m*2-2)<(n-1):
        continue
    tab=[[0 for i in range(m)] for j in range(m)]       
    tab[0][0]=1 
    fig=[1] 
    coord_X=[1] 
    coord_Y=[1] 
    L=2
        
    for r in range(m):
        for c in range(m):
            if tab[r][c]!=0: 
                continue     
            fit=True;
            rp=r+1
            cp=c+1
                 
            for num_fig in range(len(fig)):
                if (rp)==coord_X[num_fig] and (cp)==coord_Y[num_fig]:                    
                    continue
                elif (abs(coord_X[num_fig]-(rp))+abs(coord_Y[num_fig]-(cp)))<(abs(L-fig[num_fig])):
                    fit=False
                    break
            
            if fit:                
                tab[r][c]=L 
                fig.append(L)
                coord_X.append(rp)
                coord_Y.append(cp)
                L+=1                
                if len(fig)==n:                    
                    output()                    
                    raise SystemExit   
               
    if len(fig)==n:        
        output()        
        raise SystemExit